Many offshore structures contain elements with cylindrical shape, such as jacket, jack up and tension-leg platforms, marine pipelines and offshore drilling and production risers, etc. Considerable efforts have been made in recent years on developing the theoretical wake model to ensure the calculating results of current forces more accurate. However, these traditional models still have a few limitations which might lead to large errors in static or dynamic analyzing process. This study developed a new effective wake model to estimate the wake velocity distributions behind circular cylinder. The presented model was derived based on Reichardt's wake model for the time averaged wake velocity distribution. It is a combination of using Tollmien's first approximation method and Goldstein's second approximation method. Results indicate that the correction works by this paper do not make much difference when calculating the wake field at large distance. However, it will make a significant difference for the wake field close to the cylinder. The presented wake model is validated by comparing with published experimental and numerical data. Comparison results show a good reliability and stability whenever at far wake field or near wake field, broadly extends the earlier findings.
Flow over circular cylinder is a simple and useful model for many applications concerning obstacles to flow. It has been investigated for many years by numerical and experimental method. Meanwhile, the theoretical study of two-dimensional far-wake flow down stream of circular cylinders has also attracted much attention of many scholars (Blevins,2005; Fu,2017; Huse, 1992; Reichardt, 1942; Schlichting, 1930; Wu, 2002). Trace back to 1930, two-dimensional wakes were first investigated by H. Schlichting in his presented thesis (Schlichting, 1930). Schlichting's investigation, which was based on Prandtl's mixing length hypothesis, was found to be in good agreement with the experimental data that he obtained before. However, measurements showed that Schlichting's solution just constituted an approximation for very large distances. Specifically, it was only valid for x / (CD ⋅d) >50. Nevertheless, Schlichting (1979) mentioned that in the case of smaller distances it could be modified by calculating additional terms of the velocity, the terms being proportional to x−1 and x−3/2, respectively. Coincidently, a solution for the same problem which was based on Prandtl's shearing stress hypothesis was later given by H.Reichardt (1942). The two results didn’t differ much one from the other according to Schlichting's description (Schlichting, 1979). Similarly, Reichardt's wake model is not appropriate for near wake field as well (Schlichting, 2016). Some other researchers such as Huse (1992) and Blevins (2005) have also made some efforts to fix this limitation in recent years. In Fig.1, calculation results of the theoretical wake model of Reichard, Huse and Blevins are plotted against the experimental results of Nishioka (1974).
